展开 Dx[\sqrt[3]{4x^3-2}(6x^2+3)]

解答

展开

D x [3 4 x^{3} - 2 (6 x^{2} + 3)]

6 D x^{3} 3 4 x^{3} - 2 + 3 D x 3 4 x^{3} - 2

求解步骤

D x (3 4 x^{3} - 2 (6 x^{2} + 3))

去除括号:

(a) = a

= D x 3 4 x^{3} - 2 (6 x^{2} + 3)

= D x (6 x^{2} + 3) 3 4 x^{3} - 2

使用分配律:

a (b + c) = ab + a c

a = D x 3 4 x^{3} - 2, b = 6 x^{2}, c = 3

= D x 3 4 x^{3} - 2 \cdot 6 x^{2} + D x 3 4 x^{3} - 2 \cdot 3

= 6 D x^{2} x 3 4 x^{3} - 2 + 3 D x 3 4 x^{3} - 2

6 D x^{2} x 3 4 x^{3} - 2 = 6 D x^{3} 3 4 x^{3} - 2

= 6 D x^{3} 3 4 x^{3} - 2 + 3 D x 3 4 x^{3} - 2

e x p an d \frac{e ^{- 4 s} - e ^{- 6 s} + 2 s ^{2} + 8 s}{s ( s ^{2} + 4 s + 20 )}

\frac{\partial}{\partial x} ((z) (x y + x z^{3} - 2 yz))

e x p an d \frac{( x - 3 ) ( x + 4 )}{( x + 3 ) ( - x ^{3} + 9 x ^{2} - 25 x + 35 )}

e x p an d (2 x^{3} + 4 x^{2} - 5 x) l e f t (3 x y - 4 y)

e x p an d \frac{Δ x ( - 1 + y )}{y _{2} y ^{2}}